Classification into mass and periodic motionsTo arrive at a clear and insightful physicochemical interpretation of the varied complex movements and phenomena observed in nature, a simplification that retains only the most relevant features (while boldly removing the rest) is required. Therefore, we will only consider those concepts that inspired the advent of the fields of classical and quantum mechanics—mass and periodic motion. In addition, all types of motion can be expressed as a combination of linear and rotational motions, which characterise mass and periodic motion, respectively. The light unit14, capable of both linear and rotational motion, is an excellent example of this. Moreover, in a previous study that reveals the identity of quantum6, we have reported classical and quantum mechanics to be integrated concepts that are not separate from each other. From a dimensional perspective, this means that the mass expressed in classical mechanics (like in the mass-energy equivalence of Einstein’s theory of relativity, quantified by E = mc2, where E, m, and c are the energy and mass of a particle and the velocity of light, respectively)30 also has a period, while the waves expressed in quantum mechanics (like in the equation E = \(\frac{hc}{\lambda }\), where E, c, λ, and h, are the energy, velocity, and wavelength of light and the Planck constant, respectively)31 can also be expressed in units of mass. Therefore, mass and wave periods are reasonable and accessible dimensions for the analysis of unknown phenomena.To prove the mass-wave equivalence (which, by extension, translates to an equivalence between classical and quantum mechanics), we started with the assumption that the formation of a unit of mass can be traced to a biaxial revolution of a quantum particle at the velocity of light; the physical and chemical identicality6 of the meanings of the unit conversion for the Planck unit system27 is proof of the validity of this assumption. This means that in the equation E = mc2, “c2” represents the unit of mass, while “m” denotes the numerical quantity of these units. This enables a more intuitive understanding of temperature and entropy by converting their dimensions into the MS units corresponding to the Planck measurement system in a way that matches their physicochemical significance. This is simplified to retain only linear and rotational motion and, on further analysis, becomes a process of investigating which factors will remain and what significance they have when progressively evaluated till its root cause at the quantum level.Visualising the quantum states of a proton and an electronLike the previous report on quantum particles6, the initial factor causing the unit of mass formed from the revolution of two different axes, determined to be the velocity of light, as shown in Fig. 4, was derived through the following sequential steps.Figure 4Sequence of steps representing the derivation of the Boltzmann constant as a unit of entropy: (a) pure mass formed by biaxial revolution, (b) movement after removing the revolution around one of the two axes, (c) movement of one rotation during repeated revolutions, (d) visualisation of a proton as the quantum particle, (e) quantity of charge on a proton, (f) rotations involved in a single revolution, (g) movement of one rotation during repetitive rotation, (h) physical significance of considering an electron, (i) Boltzmann constant and its magnitude.First, as shown in Eqs. (1)–(2), the first-order partial derivative of energy with respect to the velocity of light eliminates revolution along one of the two axes (Fig. 4a,b).$$E = mc^{2} \;({\text{circular motion along two axes}})$$
(1)
$$\frac{\partial E}{{\partial c}} = { 2}mc\;({\text{circular motion along one axis}})$$
(2)
However, periodic revolution is still retained along the other axis. Therefore, to obtain information corresponding to the period of a single revolution, Eq. (2) is divided by the frequency (f1) as shown in Eq. (3) below (Fig. 4c):$$\left( {\frac{\partial E}{{\partial c}}} \right) \times \frac{1}{{2\pi f_{1} }} = \, 2mc \times \frac{1}{{2\pi f_{1} }} = \frac{mc}{{\pi f_{1} }}\left( {\text{circular motion of a cycle}} \right)$$
(3)
Since the frequency at this point does not represent any fixed value, it should be replaced with the number of protonic rotations (nf1) that exist in the corresponding time period. Directly substituting the mass of a proton32 in Eq. (3) yields Eq. (4). At this point, if the final calculated value of (\(\frac{{1.6 \times 10^{ – 19} \;{\text{m}} \cdot {\text{kg}}}}{{n_{f1} }}\)) is substituted by αcv, then the frequency can always be erased along with the number of rotations to yield a constant value of \(1.6 \times 10^{ – 19} \;{\text{m}} \cdot {\text{kg}}\) as shown in Eq. (5), regardless of the value of nf1. Interestingly, this coincides with the magnitude of electric charge (C) of a single proton; its units, expressed in terms of “m⋅kg”, can be considered to signify the effect (m) of one electric charge (kg) on its surroundings (Fig. 4d,e).$$\frac{mc}{{\pi f_{1} }} = \frac{{\left( {1.6726 \times 10^{ – 27} \;{\text{kg}}} \right) \times \left( {3 \times 10^{8} \;{\text{m/s}}} \right)}}{{\pi \cdot \left( {n_{f1} /{\text{s}}} \right)}} \approx \frac{{1.6 \times 10^{ – 19} \;{\text{m}} \cdot {\text{kg}}}}{{n_{f1} }}\left( {\text{calculated value}} \right)$$
(4)
$$\alpha_{{\text{cv(total)}}} = \alpha_{{{\text{cv}}}} \times {\text{number of revolutions }}\;(n_{f1} ) \, \approx 1.6 \times 10^{ – 19} \;{\text{m}} \cdot {\text{kg}}$$
(5)
From our first assumption (kg ≡ m2/s2), Eq. (5) can be finally expressed in MS units as:$$1.6 \times 10^{ – 19} \;{\text{m}} \cdot {\text{kg}} = 1.6 \times 10^{ – 19} \;{\text{m}}^{3} /{\text{s}}^{2} \;({\text{in MS units}})$$
(6)
Substituting the mass of the proton with that of the electron33 makes for a considerable departure from Eqs. (3)–(6). This is because in the case of electrons (Fig. 4f), the rotational motion corresponding to spin34,35 must also be considered, which was not required while substituting for the mass of a proton. Therefore, Eq. (3) must be divided once more by the frequency (f2) as shown in Eq. (7) below (Fig. 4g). In other words, since the number of rotations is already included in Eq. (5) when considering the proton, it is sufficient to additionally account only for electronic frequency (f2) when considering electrons. However, like in Eqs. (4)–(6), the frequency in this case does not represent a fixed value; therefore, it is replaced with the number of electronic rotations (nf2) during the corresponding time period. Directly substituting the mass of the electron33 in place of m in Eq. (7), at this point, if the final calculated value (\(\frac{{1.38 \times 10^{ – 23} \;{\text{m}} \cdot {\text{kg}} \cdot {\text{s}}}}{{n_{f2} }}\)) is substituted with \(\beta_{{{\text{cv}}}}\), then the frequency can always be erased along with the number of rotations to yield a constant value as shown in Eq. (8), regardless of the value of nf2.$$\frac{mc}{{\pi f_{1} }} \times \frac{1}{{2\pi f_{2} }} = \frac{{\left( {9.1093 \times 10^{ – 31} \;{\text{kg}}} \right) \times \left( {3 \times 10^{8} \;{\text{m/s}}} \right)}}{{2\pi^{2} \cdot \left( {n_{f1} /{\text{s}}} \right) \cdot \left( {n_{f2} /{\text{s}}} \right)}} \approx 1.38 \times 10^{ – 23} \;{\text{m}} \cdot {\text{kg}} \cdot {\text{s}}\;\left( {\text{calculated value}} \right)$$
(7)
$$\beta_{{{\text{cv}}\left( {{\text{total}}} \right)}} = \beta_{{{\text{cv}}}} \times {\text{number of rotation}}\; \, \left( {n_{f2} } \right) \, = \beta_{{{\text{cv}}}} \times n_{f2} \approx 1.38 \times 10^{ – 23} \;{\text{m}} \cdot {\text{kg}} \cdot {\text{s}}$$
(8)
As above, substituting our assumption (kg ≡ m2/s2) into Eq. (8), it can finally be expressed in terms of MS units, as shown in Eq. (9) (Fig. 4h):$${1}{{.38 \times 10}}^{ – 23} \;{\text{m}} \cdot {\text{kg}} \cdot {{s = 1}}{{.38 \times 10}}^{ – 23} \;{\text{m}}^{{3}} /{\text{s}}\;({\text{in MS units}})$$
(9)
Just as the value calculated from the mass of the proton is numerically equal to the charge on the proton, the value calculated above from the mass and spin of the electron is numerically equal to the Boltzmann constant36 (Fig. 4i). The final result here can be said to be the state of a pure electronic unit in which electrons rotate only once, and this is the meaning of the Boltzmann constant. Although exactly, \(1.38 \times 10^{ – 23}\) is only the same magnitude, the meaning can be approximated based on the Planck unit conversion25. Since the Boltzmann constant has the same dimensions as the volumetric flow rate6, it is estimated to be about the smallest unit of electromagnetic wave (light with almost linear motion and almost no wavelength)37 that can flow per unit time.Significance of the Boltzmann constantSince we approximated the Boltzmann constant as a form of “light with almost linear motion and no wavelength”, it has to be verified to determine its applicability elsewhere. Therefore, its consistency was examined when applied to a light model14 that includes the behaviour of electromagnetic waves. For this, a model featuring a cone-shaped unit of light that embodies all of the duality of light—with a mass corresponding to a particle at its front and a period corresponding to a rotation at its rear—was first proposed (Fig. 3b). The energy corresponding to each part of this unit can be visualised as a cone-shaped structure (Fig. 3a) and quantified as shown in Eq. (10)14, where me and mp are the masses of an electron and a photon, respectively.$$E{\text{ (total light energy)}} = \frac{{4\pi^{3} r(r – a)^{2} }}{\lambda \tan \theta } m_{{\text{e}}} c^{2} {\text{(wave energy)}} + \frac{1}{2} m_{{\text{p}}} c^{2} {\text{(particle energy)}}$$
(10)
However, since electrons rotate in addition to their revolution, this model accounts for a state of motion in which the electrons simultaneously rotate and revolve (Fig. 4f). Additionally, light moves simultaneously in two directions (Fig. 5a)—one being that of its propagation, along which it reaches the velocity of light, and the other in the transverse direction, along which it does not reach the velocity of light (Fig. 5a,b)—with its energy accounting for the effect it has on its surroundings. If the unit movement along the transverse axis also attains the velocity of light, then it embodies mass (kg = c2 = m2/s2, where c, m, and s denote the velocity of light and the units of metre and second, respectively) (Fig. 5c).Figure 5Various cases where the Boltzmann constant was applied as an electromagnetic wave unit to the model of light: (a) a typical model of light rotating along two axes, of which only one reaches the velocity of light, (b) the model of light when the velocity of rotation along the other axis also approaches that of light, (c) mass unit formed when rotation along both axes reaches the velocity of light, (d) typical wavelength in a general light model such as (a), (e) wavelength on one of the axes approaching the velocity of light, (f) wavelength when the velocity of the other axis increases, (g) wavelength at which the velocity of the other axis nearly reaches the speed of light, (h) mass unit formed by c2 as in (c).When this process is described sequentially, the steps are as follows.First, the wavelength is represented as displayed in Fig. 5d. The shorter the wavelength, the shorter the distance travelled by the wave (as shown in Fig. 5f), and the denser it becomes. Therefore, when the wavelength reaches its limiting value as the velocity of the wave approaches that of light, it can be regarded as an area (Fig. 5e,g). At this point, Fig. 5e is the velocity of light from the beginning in the horizontal direction of light, whereas Fig. 5g depicts a scenario where the velocity of the wave has not yet reached that of light; Fig. 5a,b, on the other hand, depict cases where it gradually increases to approach that limit in the transverse direction. Therefore, when the revolution of the particle around both axes has completely reached the velocity of light, the mass is made up of a closed curve, as shown in Fig. 5h.However, the electrons that make up light simultaneously revolve in a screw-like motion (representative of its electrical properties) along the direction of propagation of light and rotate in a spin-like motion (representative of its magnetic properties) in the transverse direction38,39,40. Therefore, it is believed that the rotation and revolution of an electron are representative of its electrical and magnetic properties; however, since these two motions occur simultaneously, electricity and magnetism, too, are concurrent phenomena and can be treated as a unified electromagnetic phenomenon.As already mentioned above, we were able to deduce the exact magnitude of the Boltzmann constant (in units of m3/s) while considering the dual influence of electronic rotation and revolution. This implies that after conversion to the Planck system of unit27, the entropy (J/K) can be expressed in terms of m3/s. Therefore, if the concept of entropy is applied to the light model, an increase in entropy can be inferred from a corresponding increase in the number of Boltzmann constants or in the rotation of the rear part of the light unit.Geometric significance of temperatureEven though the complete meaning of the currently existing concept of temperature cannot be accurately grasped, we can express it in MS by the Planck unit conversion27. As mentioned in our previous report26, there exists the possibility of temperature (T) and entropy (S) being related to each other by means of a hysteresis loop, specifically in terms of energy expressed as TS—in order to increase energy, only either one (but not both) of T or S may be increased at a given time. However, since the identity of S is not clear, there has been little use for it, due to which it has been common to increase the phenomenologically detectable T41,42,43 alone in most cases.This means that in the relationship of E = TS, when energy (E, in units of m5/s4) is divided by entropy (m3/s), temperature can be expressed as m2/s3, as shown in Eq. (11) below:$${\text{T }}\left( {{\text{m}}^{{2}} /{\text{s}}^{{3}} } \right) \, = E\left( {{\text{m}}^{{5}} /{\text{s}}^{{4}} } \right) \, /S\left( {{\text{m}}^{{3}} /{\text{s}}} \right)\;({\text{in MS units}})$$
(11)
While the equivalent extended MS system of units (Fig. 6)6 assigns temperature with the same dimensions as magnetic field strength and dynamic viscosity, it is still difficult to recognise the intuitive concept of temperature. To make it easier, as shown in Eq. (12) below, the MS unit needs to be considered by dividing it into its constituents of pure mass (in terms of kg ≡ m2/s2)—i.e., mass without any external influence, as shown in SI, Fig. S1a—and frequency.$${\text{T}}\left( {{\text{m}}^{{2}} /{\text{s}}^{{3}} } \right) \, = {\text{ kg }}\left( {{\text{m}}^{{2}} /{\text{s}}^{{2}} } \right) \times {\text{frequency }}\left( {{1}/{\text{s}}} \right)\;({\text{in MS units}})$$
(12)
Figure 6Extended MS unit system including various physical meanings.Equation (12) can be regarded as a representation of a unit of mass vibrating and propagating around (SI, Fig. S1b). Thus, the temperature indicates when a unit of mass begins to vibrate, and any increase in temperature means that these vibrations go correspondingly farther (SI, Fig. S1c).This geometric perspective seems to dovetail well with established concepts, meaning that our proposed approach to identify quantum particles, light, and TS energy is very likely to be a fundamental principle rather than a long shot. Therefore, by intuitively recognising these principles, we have successfully presented a basis to further expand the range of applications of temperature and entropy.
Physical interpretation of entropy, Boltzmann constant, and temperature
